According to the method of least squares, the line of best fit is the one that minimizes the squares of the differences between the data points' observed (experimental) y-values and their expected (theoretical) y-values. This line is known as the least squares regression line.

To calculate the sum of squares of a line, find the expected y value of each point by substituting the corresponding x value into the linear regression equation. Then, find the difference between the observed y value and the expected y value for each point. Finally, square the difference between the observed and expected y value for each point, and then sum those values. The lines that were shown on the previous page are calculated below:

Point

x

Observed y

Expected

lines A; B; C

Difference y-

lines A; B; C

Difference Squared (y-)2

lines A; B; C

1

10

5.0

8.0; 10.0; 12

-3.0; -5.0; -7.0

9.0; 25.0; 49.0

2

18

24

14.4; 18; 22

9.6; 6.0; 2.0

92.16; 36.0; 4.0

3

38

27.5

30.4; 38; 45

-2.9; -10.5; -17.5

8.41; 110.25; 306.25

4

50

60.0

40.0; 50.0; 60.0

20.0; 10.0; 0

400.00; 100.0; 0

5

63

50.0

48.0; 63; 74

2.0; -13.0; -24.0

4.00; 169.0; 576

The total sum of squares for line A = 513.57; line B= 440.25; line C= 935.25. As said before, the line that minimizes this value is the line of best fit according to the least squares method. Therefore, line B is the best fit of these 3 lines.